Equations and Graphs of Circles 2024

Front

What is the standard equation of a circle?

Back

The standard equation of a circle is (x-h)² + (y-k)² = r², where (h, k) is the center and r is the radius.

Front

How do you find the center of a circle from its equation?

Back

The center of a circle in the equation (x-h)² + (y-k)² = r² is given by the point (h, k).

Front

What does the radius of a circle represent in its equation?

Back

The radius (r) in the equation (x-h)² + (y-k)² = r² represents the distance from the center of the circle to any point on the circle.

Front

If the equation of a circle is (x+3)² + (y-2)² = 16, what is the radius?

Back

The radius is 4, since r² = 16, thus r = √16 = 4.

Front

What is the center of the circle given by the equation (x-1)² + (y+5)² = 9?

Back

The center is (1, -5).

Front

How do you determine if a point lies inside, on, or outside a circle?

Back

Calculate the distance from the center to the point. If the distance is less than the radius, the point is inside; if equal, on; if greater, outside.

Front

What is the equation of a circle with center (0, 0) and radius 5?

Back

The equation is x² + y² = 25.

Front

In the equation (x-2)² + (y+3)² = 36, what is the center and radius?

Back

The center is (2, -3) and the radius is 6.

Front

What is the effect of changing the value of h in the equation (x-h)² + (y-k)² = r²?

Back

Changing h shifts the circle left or right along the x-axis.

Front

What happens to the circle's size if the radius is increased?

Back

The circle becomes larger as the radius increases.